What do normative indices of multidimensional inequality really measure?

•Normative multidimensional inequality indices measure both inequity and inefficiency.•We provide a decomposition of inequality into inequity and inefficiency.•Strikingly, the inequity component turns out to be a so-called two-stage measure.•The decomposition clarifies controversies surrounding two prominent transfer axioms.•An application to inequality in human development illustrates the analysis.

We argue that normative indices of multidimensional inequality do not only measure a distribution's extent of inequity (i.e., the gaps between the better-off and the worse-off), but also its extent of inefficiency (i.e., the non-realized mutually beneficial exchanges of goods). We provide a decomposition that allows us to quantify these two parts of inequality. Strikingly, the inequity component turns out to be a two-stage measure, that is, a measure that applies a unidimensional inequality measure to the vector of individual well-being levels. The decomposition also clarifies existing controversies surrounding two prominent transfer axioms, viz., uniform majorization and correlation increasing majorization. An application to inequality in human development illustrates the analysis.